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To help students visualize abstract concepts Introduce a new topic; students then can discover the algebra rules instead of being told by the teacher Reinforce a topic for a struggling student

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Positive TilesNegative Tiles 11 1 1 x x X x x X X² 11 X

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Addition and Subtractions of Integers Distributive Property Combining Like Terms Solving Equations Multiplying Binominals Factoring Polynomials

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3 + ( -5 ) = ? Additions means Combine Use the zero property to cancel/take away a pair of blue and red tiles Left with 2 -1 tiles Answer = -2 1 1 1 1 1 1 1 1

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5 – (-2) = ? Start with 5 take away Answer = 7 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Now you can take away 2 -1 tiles Add a zero pair in order to be able to take away 2 - 1 tiles

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3 (2x + 1) is equivalent to 6x + 3 3 (2x + 1) {using repeated addition) Rearrange the tiles XX 1 XX XX 1 1 X X X X X X 1 1 1 + +

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(x² - 2x -3) – (2x² + x – 2) = ? X² X X 1 1 1 Subtraction would be represented by adding the opposite of each term in parenthesis X² X 1 1 Cross out all zero pairs, what you have left over is your answer Answer = -x² – 3x – 1 +

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2x -2 = 4 X X 11 = 1111

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Add two tiles to the left to make a zero pair * To keep scale balanced - do the same to both sides * X X 11 = 1111 1111

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2x -2 = 4 Arrange the tiles into groups Answer: X = 3 1 1 X = X 1 11 1

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(x + 3) (x + 2) X111 1 X 1 L W

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X111 1 X 1 X² XXX X X 111 111 Answer = x² + 5x + 6 Fill in the space so that lines between tiles are continuous

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2x² + 5x + 3 X² X X XX X111 First fill in the x² tiles and 1 tiles Then arrange the x tiles to match

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2x² + 5x + 3 X² X X XX X111 111 1 XX X x + 1 2x + 3 Answer = (2x +3) ( x + 1)

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Teaching the rules of Algebra Tiles Multiplying a Polynomial by a Binomial More difficult using negative number for: Distributing Factoring Multiplying two binomials (It is possible but students might struggle)

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Visualizing an abstract concept Students generating rules Practice with basic problems then have students find patterns to then apply to more challenging problems Another tool in the tool box

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Algebra Tiles – Completing the Square

Algebra Tiles – Completing the Square

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